Решить систему: x^2*y^3=16 y^2*x^3=2

[latex]left { {{x^2y^3=16 (1)} atop {y^2x^3=2 (2)}} ight.[/latex] разделим  (1) на (2) [latex]left { {{frac{y}{x}=8} atop {y^2x^3=2}} ight.<=>left { {y=8x} atop {(8x)^2x^3=2}} ight.<=>left { {y=8x} atop {64x^5=2}} ight.<=>left { {y=8x} atop {x^5=frac{2}{64}} ight.<=>\ \ <=>left { {y=8x} atop {x^5=frac{1}{32}} ight.<=>left { {y=8x} atop {x=frac{1}{2}} ight.<=>left { {y=8*frac{1}{2}} atop {x=frac{1}{2}} ight.<=>left { {y=4}} atop {x=frac{1}{2}} ight.[/latex]

x^2*y^3=16 y^2*x^3=2   y/x=8 y=8x   (8x)^2*x^3=2   64x^2*x^3=2   64x^5=2   32x^5=1   x^5=1/32 x=1/2   y=8*1/2=4 y=4 Ответ:(1/2,4)